Multilevel Delayed Acceptance MCMC

We develop a novel Markov chain Monte Carlo (MCMC) method that exploits hierarchy of models increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the rewrites multilevel MCMC approach Dodwell et al. [SIAM/ASA J. Un-certain. Quantif., 3 (2015), pp. 1075–1108] in terms delayed acceptance Christen and Fox [J. Comput. Graph. Statist., 14 (2005), 795–810]. In particular, is extended use arbitrary depth allow subchains length. show algorithm satisfies detailed balance hence ergodic for Furthermore, variance reduction derived multiple levels subchains, adaptive correction coarse-level biases developed. Three numerical examples Bayesian inverse problems are presented demonstrate advantages these methods. The software available PyMC3.